+474 How many unique sums can be formed by adding any three different numbers from the set {4,6,8,10,12,...,154}?
+1622 The smallest number that can be formed is 4 + 6 + 8 = 18, and the largest: 150 + 152 + 154 = 456.
Note how every even number up to 456 can be formed: for example, 20 = 18 + 2 = 4 + 6 + 8 + 2 = 4 + 6 + 10... 164 = 4 + 6 + 154
166 = 4 + 8 + 154... 168 = 6 + 8 + 154... 170 = 6 + 10 + 154... so on- until you reach the largest number that can be formed.
Okay, so now we know that all the even numbers 18 to 456 inclusive can be formed: how many numbers are in this list?
# of numbers {18,..., 456} = # of numbers {18 - 18,...,456 - 18 = 438} = {0/2,...,438/2} = {0,...,219} = {0 + 1,...,219 + 1} = 1 through 220 inclusive.
So, the answer is 220.
+1622 The smallest number that can be formed is 4 + 6 + 8 = 18, and the largest: 150 + 152 + 154 = 456.
Note how every even number up to 456 can be formed: for example, 20 = 18 + 2 = 4 + 6 + 8 + 2 = 4 + 6 + 10... 164 = 4 + 6 + 154
166 = 4 + 8 + 154... 168 = 6 + 8 + 154... 170 = 6 + 10 + 154... so on- until you reach the largest number that can be formed.
Okay, so now we know that all the even numbers 18 to 456 inclusive can be formed: how many numbers are in this list?
# of numbers {18,..., 456} = # of numbers {18 - 18,...,456 - 18 = 438} = {0/2,...,438/2} = {0,...,219} = {0 + 1,...,219 + 1} = 1 through 220 inclusive.
So, the answer is 220.
